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591.
Hardin Douglas P. Hogan Thomas A. Sun Qiyu 《Advances in Computational Mathematics》2004,20(4):367-384
We use the matrix-valued Fejér–Riesz lemma for Laurent polynomials to characterize when a univariate shift-invariant space has a local orthonormal shift-invariant basis, and we apply the above characterization to study local dual frame generators, local orthonormal bases of wavelet spaces, and MRA-based affine frames. Also we provide a proof of the matrix-valued Fejér–Riesz lemma for Laurent polynomials. 相似文献
592.
Alexandr Kostochka 《Random Structures and Algorithms》2004,24(1):1-10
Let m(r, k) denote the minimum number of edges in an r‐uniform hypergraph that is not k‐colorable. We give a new lower bound on m(r, k) for fixed k and large r. Namely, we prove that if k ≥ 2n, then m(r, k) ≥ ?(k)kr(r/ln r)n/(n+1). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
593.
Summary Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines
and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations.
Functional limit theorems for such random processes are obtained. 相似文献
594.
595.
In this paper we consider a class of semilinear Schrödinger equation which terms are asymptotically periodic at infinity. Under a weaker superquadratic condition on the nonlinearity, the existence of a ground state solution is established. The main tools employed here to overcome the new difficulties are the concentration-compactness principle and the Local Mountain Pass Theorem. 相似文献
596.
597.
In this paper, we prove a bifurcation phenomenon in a two-phase, singularly perturbed, free boundary problem of phase transition. We show that the uniqueness of the solution for the two-phase problem breaks down as the boundary data decreases through a threshold value. For boundary values below the threshold, there are at least three solutions, namely, the harmonic solution which is treated as a trivial solution in the absence of a free boundary, a nontrivial minimizer of the functional under consideration, and a third solution of the mountain-pass type. We classify these solutions according to the stability through evolution. The evolution with initial data near a stable solution, such as the trivial harmonic solution or a minimizer of the functional, converges to the stable solution. On the other hand, the evolution deviates away from a non-minimal solution of the free boundary problem. 相似文献
598.
We prove that the vertex degree threshold for tiling (the 3‐uniform hypergraph with four vertices and two triples) in a 3‐uniform hypergraph on vertices is , where if and otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling. 相似文献
599.
Alexander Tiskin 《Discrete Mathematics》2007,307(16):1973-1981
In 1984, Stein and his co-authors posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By definition, a tripod of order n is formed by a corner and the three adjacent edges of an integer n×n×n cube. How densely can one fill the space with non-overlapping tripods of a given order? In particular, is it possible to fill a constant fraction of the space as tripod order tends to infinity? In this paper, we settle the second question in the negative: the fraction of the space that can be filled with tripods must be infinitely small as the order grows. We also make a step towards the solution of the first question, by improving the currently known asymptotic lower bound on tripod packing density, and by presenting some computational results on low-order packings. 相似文献
600.
杨健夫 《南昌大学学报(理科版)》1989,13(2):1
本文考虑RN(N>2)上的椭园方程-△u=f(x,u)正解的存在性。对于f(x,u)关于u在零和无穷附近如同u(N+2)/(N-2)的增长的情形,得到了正解存在性的结果。 相似文献